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2013
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    Self-oscillations in implicit singularly perturbed dynamical systems on the plane

    2014, Vol. 10, No. 2, pp.  157-175

    Author(s): Gotsulenko V. V.

    To implicitly singularly perturbed autonomous systems of ordinary differential equations of second order found some sufficient conditions for the existence of periodic solutions of relaxation (self-oscillation), determined by means of an auxiliary dynamical system that implements a sliding mode. It is shown that so defined periodic motions have typical properties of self-oscillations of relaxation defined autonomous systems of ordinary differential equations with a small parameter at the highest derivative.



    Keywords: implicitly singularly perturbed system, sliding mode, the relaxation periodic solution, self-oscillations
    Citation: Gotsulenko V. V., Self-oscillations in implicit singularly perturbed dynamical systems on the plane, Rus. J. Nonlin. Dyn., 2014, Vol. 10, No. 2, pp.  157-175
    DOI:10.20537/nd1402003


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